Detection of Artificial Satellites in Images Acquired in Track Rate Mode.

Detection of Artificial Satellites in Images Acquired in Track Rate Mode. Martin P. Lévesque Defence R&D Canada- Valcartier, 2459 Boul. Pie-XI North, Québec, QC, G3J 1X5 Canada, martin.levesque@drdc-rddc.gc.ca Presented to: Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, September 13-16, 2011 ABSTRACT For surveillance of space purposes, satellites must be re-observed periodically to measure their positions and update their orbital parameters. This represents an incredible volume of data for which an automatic processing capability is desired. Previous developments [1,2,3] produced automatic detection algorithms for images acquired in Step Stare mode (SSM) with sidereal tracking. However, it was proven that the track rate mode (TRM) is more sensitive. Hence, the algorithmic framework was redesigned and applied to this mode. When an imaging sensor tracks a satellite (or a satellite cluster), the stars appear as streaks while the satellites are point-like objects. A series of algorithms was developed for the detection of satellites and star streaks. The centroids of the star streaks are detected first. They are necessary for the astrometric calibration of the image. Thereafter, the satellites are detected using two possible scenarios; they are detected with the maximum of sensitivity against the dark sky background, or they are detected with the contrast criteria if they are overlapping star streaks. This algorithm framework automatically extracts all required information from the image and adapts the processing parameters and strategy consequently, so no a priori knowledge is require for their execution. INTRODUCTION: The maintenance of the Space Surveillance Network (SSN) catalogue of space resident objects (RSO) requires an incredible amount of fresh observations. Thousands of objects need to be observed almost every month. This is done by several observatories which must acquire hundreds of observations every night. This represents a huge amount of image data that must be analyzed and reduced to observation update reports. This can be done completely automatically with the appropriate processing facilities. 1-1

The goal of the recent sensor development is the creation of autonomous observatories which could do the entire job automatically [4]. Ultimately, they should be operated by a single person, who checks the system status, error reports and consistency of observation reports. Presently, this goal is achieved. When TLEs (Two lines element set) become too old, new observation requests are transmitted to the sensor operating center and the scheduler program generates the observation tasks. This program determines when a RSO will be observable by a specific observatory, generates sequences of command lines that will control the dome, telescope mount and camera shutter. These command sequences are uploaded into the observatory controlling computer. Once the observatory has performed its task, the images are downloaded and processed with the automatic detection algorithms presented in this paper. The detections are reported to SSN and the TLE database is updated. Presently, all these process can be done completely automatically. The RSO observation can be done in several different modes. Automatic image processing algorithms [1,2,3] were developed for the step stare mode (SSM), i.e., the sidereal tracking mode. But this acquisition mode is not used anymore because the track rate mode (TRM) is more sensitive and is now almost the only widely-used acquisition mode. Therefore, the processing scheme had to be rearranged [6] for these images where stars make streaks and where satellites appear like points. In this new image processing framework, the image background is still removed first [5]. After, the star streaks are filtered and detected. Once the stars are adequately filtered, they are removed from the background-free image and the remaining point objects become apparent and easily detectable. This paper presents an overview of this processing. IMAGE and PROCESSING MODEL: The model for the original image is: I 0 = B + S + O + n B: Background (or flat field) S: Star streaks O: RSO n: noise 1-2

Once the background is estimated «B» and removed, the background free image I -B is: where the background residue R B is negligible (R B = B - «B»). I -B = I 0 «B» = S + O + R B + n. I 0 original image - «B» - background estimate = I -B = background free image Then, knowing the star streak length and orientation (s l, s θ ), a matched filter M [1,2] provides a very clean estimation of the streaks «S» which is noise free and where the possible overlapping point objects (tracked RSO) are clipped. This matched filter function also provides the image C which is the result of the convolution of the streak «S» by the streak model s(s l, s θ ), a line segment with the streak length and orientation. [«S», C] = M (I -B, s(s l, s θ ) ). 1-3

After removing the streak estimation «S», the resulting streak-free image I-S is dominated by the remaining RSOs: I-S = I-B - «S» = O + RB + RS + n. I-B background free image «S» filtered streaks Inserted pattern with controlled A real satellite SNR for sensitivity testing. overlapping a star streak. Defence R&D Canada 1-4 note:(rs = S - «S») I-S = O + RB + RS + n. = RSOs + processing residues + noise

STAR DETECTION: The positions of the detected RSOs are done relative to the position of the known close stars (astrometric calibration). Hence, enough stars have to be detected and the position of their centroids measured. With enough stars, software like PinPoint [7] can calculate the conversion of pixel coordinates into real sidereal coordinates. DETECTION OF STREAK LENGTH AND ORIENTATION (s l, s θ ): There are enough star streaks in the image to be able to automatically extract their parameters. Streaks are all alike and they are similar to a rectangle function. Consequently, the profile of the Fourier transform is dominated by the sin(x)/x function. The absolute value of the FFT gets rid of the e iθ phase factor (in the Fourier plane) and preserves only the profile common to all streaks. With a directional signal summation (done with a Radon transform), the highest contrasted profile is obtained when the modulation are well align with the integration direction. Hence, the maximum of the Radon transform indicates the orientation s θ of this pattern. Image in TRM ABS ( FFT ( image )) The profile of the Radon transform in the streak orientation s θ shows the sin(x)/x function profile, which is the typical Fourier transform of the rectangle (streak) function. The FFT measurement of the zeros (or minima and maxima) allows the calculation of the length of the streaks s l. Image 1 Image 2 Radon ( ABS ( FFT ( image))) Extracted profile at 145 degrees 145 degrees Maximum intensity of the extracted angle-dependent profiles Integrated Central Radon profile 145 degrees 2-1 Angles (degrees) With (s l, s θ ) known, the streak can be model and matched filter (I -B, s(s l, s θ ) ) can be computed.

MATCHED FILTER AND STAR STREAK MEASUREMENT With the known streak parameters, the iterative matched filter [1,2] is able to provide a clean view of the streaks, with reduced noise and clipped overlapping RSOs. This is illustrated in the following figure. Bright streak Faint streak Original streaks Streak model: s(s l, s θ ) Streak convolved by the streak model; C = I -B s(s l, s θ ) Filtered streaks «S» = min(i -B, 2C) (Refs. 1,2) Profiles: Red line: streak profile Blue line: convolution peak profile Mean value Bright star Threshold set at 1σ n Faint star centroid The streak length (previously estimated with the modulation of the Fourier transform) can be validated with the length measured at halt height of very bright streak. The maximum of the convolution peak provides the mean value of the streak intensity. This is an easy way to measure intensity of very faint streaks because this convolution peak is still clearly measurable for objects with intensity comparable to the noise level. The position of the maximum of the convolution peak also corresponds to the position of the streak centroid. 2-2

Extracting individual streak and measuring star position and intensity: All streaks are separated into individual object with a binary mask, which is obtained by clipping the image above a low value threshold. The streak centroid (center of intensity), intensity and length is measured for every object. Binary masks can be done from filtered streak «S» (with limited faint star extraction capability) or from convolved streak C (it merges close bright streaks). Filtered streaks The extraction solution consists in using a two-pass algorithm. The bright stars are extracted first with the sharp mask A. Very often, there are not enough bright streaks for the establishing of a valid astrometric solution. Therefore, the first detected stars are erased from the image, the image is refiltered and a new binary mask B is created for the extraction of fainter stars. The detection limit is SNR > 1. Usually, this provides enough stars for positioning reference. Intensity Mask A: made with filtered streaks «S» > 2σ n Mean length in pixels Profile coordinates in pixels Perpendicular profile Intensity PSF width Mask B: made with convolved streaks C > 1σ n Pixel Mask A: First detected stars erased Mask B: for faint stars Two-steps star detection Bright stars extracted and detected with mask A: Re-filters image Faint stars extracted and detected with mask B: 2-3

Unmerging merged streaks: A current issue is that, very often, several streaks overlap each other and are extracted as a single object. The processing facility is able to deal with these objects. A merging case is detected when the size of the extraction box is oversize (length of the window diagonal) or when the centroid (the maximum of the convolution peak) is far away from the box center (centroid error). When this occurs, the first detected star is erased and the algorithm search for another one. The process continues until what remains is only noise or processing artefacts that do not have the appropriate profiles. expected length object length Two close streaks merged by their extraction mask... first maximum geometric center... and their equivalent convolution peaks (truncated by the extraction mask) model Here is the modeled of the convolution peak. Its intensity is scaled to match the intensity of the detected object, and center on its position. model centered here and subtracted second maximum After subtraction of the peak model, it remains only the peak of the second object. Example of unmerged streaks: the first detections are marked with a yellow crosshair. Red crosshairs indicate following streaks that were detected with the unmerging process. 2-4

RSO detection: The RSO detection depends of two factors: 1) the image PSF and 2) the image background, which can be the dark sky or an overlapping start streak. For a very sharp PSF (less than one pixel), the basic detection threshold, in the streak-free image I -S is set to 9σ n ; Basic detection: I -S > 9σ n This high threshold value prevents the declaration of false alarm cause by noise (more or less Gaussian) produced by the CCD sensor and the ADC. Hence, only detections with almost 100% of probability of being a real target are declared. For larger PSF width w PSF, the local average «I -S» wpsf, estimated over the PSF area (w PSF x w PSF pixels) provides a better SNR. The detection declaration is done with: PSF adapted detection: «I -S» wpsf > 9σ n / w PSF. If there is an overlapping star streak, the contrast ratio between the tracked RSO and the star streak is now the dominant factor. The modified detection condition is now: Detection in presence of overlapping streak: «I -S» wpsf > 2 «S» + 9σ n / w PSF, where «S» the best estimate of the RSO brightness of the overlapping streak. Experiments showed that a single contrast ratio «S» generates several false alarms, but the ratio 2«S» has proven to be adequate. This test is done in three steps. - Test 1: A pixel-to-pixel comparison is done by using the (smooth with the local average) streak-free image «I -S» with the image of filtered streaks «S» provided by the matched filter. Note that in absence of streak, this detection condition is only limited by the noise level. But, in the presence of streaks, the contrast ratio is dominant. Unfortunately, even with the contrast criteria, too many false alarms are raised in the streak areas. These alarms must be checked again with the following more restrictive conditions. - Test 2: An object-to-object comparison is done. Due to the quantization of the signal, streak pixels have strong intensity fluctuations. This produces high value pixels on the streak edges, where the signal should be faint (PSF profile). Therefore, the previous detection condition has a tendency of generating false alarms on the streak contour. But these alarms are usually fainter that the streak-mean value. Hence, for a declared alarm, a verification is performed to see if the alarm overlapped a streak (inside a streak binary mask A) and its intensity is compared with the value of the corresponding streak. This eliminates all false alarms produced by normal signal fluctuations over the faint contour. 3-1

- Test 3: For the remaining alarms, a last test verifies if this alarm is just beside a streak and in the PSF range. It often occurs that false alarms are just beside a streak, without being included into its mask. Then the object-to-close-object intensity comparison is done. This eliminates all remaining close-to-a-streak false alarms. At the end, only alarms with significant contrast are reported as valid detections. Examples: filtered streak raw streak eliminate by test 1 eliminate by test 3 eliminate by test 2 Results: Detected satellites Detected star streaks DETECTED STARS: DETECTION REPORT PSF width: 2.3 Streak length: 24.0 rank bright- object length of position centroid PSF merged ness index window line column position stars? diagonal error 1 37979 60 98 165 116 31.1 2.46 y 2 9850 263 72 117 441 12.5 2.40 y 3 8593 305 55 200 476 12.2 2.96 y 4 8328 70 52 638 139 4.5 2.49. 5 6996 432 35 26 639 0.5 2.98. DETECTED SATELLITES: PSF width: 2.3 index SNR Position sat/streak line sample ratio 49 95.3 291 180 12.5 60 438.1 320 246 11.2 2 detected satellites. Rejected detections index SNR Position sat/streak cause of line sample ratio rejection 1 55.6 4 2 6.8 :truncated by image border 2 6.5 218 2 1.7 :faint ratio These images illustrate the result of all the processing described previously. This image was acquired in the galactic plane. For an accurate astrometric calibration of the image, the galactic plane should be avoided because it is difficult getting a unique solution for the recognition of the star pattern (too many stars). But this is an excellent test image. The PSF and streak length and orientation are calculated with the image content. The detection thresholds are set consequently and two RSOs are detected and reported. The crosshairs indicate the 3-2

centroids of the detected star streaks. The color code indicates how they are detected. Yellow means the bright streak is detected in the first step with the binary mask A. Red means the streak is detected with the unmerging process. Yellow is for the faint streaks detected in the second step with the binary mask B, recalculated after the first-detected bright-streak are erased. Comparison of sensitivity for images acquired in TRM and SSM: In previous works (ref. 1,2,3), algorithms were developed for the detection of satellite streaks in image acquires in SSM (Step Stare Mode), i.e. the usual sidereal tracking. The method is very sensitive and streaks can be detected with very low detection threshold, lower than the detection threshold used for the TRM. But, in TRM, the RSO brightness is concentrated on a few pixels only, rather than being spread over a long streak. The question is: which method is the most sensitive? The following table shows how much energy (or intensity in pixel count) is required for the satellite to be able to succeed in the detection tests. Definitively, the acquisition in track rate mode is by far very more sensitive than the SSM, almost by a factor of 5 (2 magnitudes more sensitive). Acquisition mode PSF (pixel) Streak length Detection condition Total energy (in pixel count) required to be detected TRM 1 - I -S > 9σ n 9σ n TRM 3 - «I -S» (3x3) > 3σ n 45σ n SSM 3 50 pixels Convolution peak > σ n 160σ n SSM 3 130 pixels Convolution peak >0.5 σ n 206σ n Conclusion: No a priori knowledge is required by the algorithms presented here for detection in TRM mode. All required information is extracted from the image content. They are the PSF width, noise level and streak length and orientation. Once the streak morphology is known, the star streaks are filtered, detected and reported for the calculation of the astrometric calibration, and removed for the detection of point objects. 3-3

The star detection method is very sensitive. Almost all star streaks with a SNR>1 are detected. Merged streaks can be unmerged if their separation is greater than half a streak length or width. This permits obtaining enough stars of reference for the transformation of pixel coordinates into sidereal coordinates, even in a poor star field. The tracked-satellites detection method is also very sensitive, but its sensitivity is limited to avoid declaration of false alarm. This method is self adapting to the noise level, PSF width and to the presence or not of overlapping star streaks. Satellite detection algorithms have been developed for both SSM and TRM acquisition mode. Both set of algorithms reach the limit of detection imposed by the noise. In both case, the detection threshold are adjusted to avoid declaration of false alarms. Comparison of both methods indicates clearly that the TRM acquisition and processing methods are more sensitive by an order of two magnitudes. This was known by instinct, but now the acquisition and processing experiments are completed and numbers support the hypothesis. References: 1. Lévesque M.P.,: Automatic Reacquisition of Satellite Positions by Detecting Their Expected Streaks In Astronomical Images, 2009 AMOS Technical Conferences, 02 Sept. 2009, proceeding: 10 pages. 2. Lévesque M. P., Buteau S., Image Processing Technique for Automatic Detection of Satellite Streaks. DRDC Valcartier 2005 TR-386. Defence R&D Canada Valcartier. http://cradpdf.drdc.gc.ca/pdfs/unc64/p527352.pdf, accessed Apr. 2011. 3. Lévesque M. P., Lelièvre M., Improving satellite-streak detection by the use of false alarm rejection algorithms. DRDC Valcartier TR 2006-587. Defence R&D Canada Valcartier. http://pubs.drdc.gc.ca/pdfs/unc76/p530206.pdf, accessed Apr. 2011. 4. Wallace B., Rody J., Scott R., Pinkney F., Buteau S., Lévesque M. P., A Canadian Array of Ground-Based Small Optical Sensors for Deep Space Monitoring, 2003 AMOS Technical Conference. 5. Lévesque M. P., Lelièvre M., Evaluation of the iterative methods for image background removal in astronomical images. DRDC Valcartier TN 2007-344. Defence R&D Canada Valcartier. http://pubs.drdc.gc.ca/pdfs/unc69/p52905 4.pdf, accessed Apr. 2011. 6. Lévesque M. P., Image processing algorithms for the automatic detection of artificial satellites acquired in track rate mode (TRM). DRDC Valcartier TR 2010-052. Defence R&D Canada Valcartier. Limited distribution, in publication. 7. http://pinpoint.dc3.com/, accessed Apr. 2011. R & D pour la défense Canada 3-4